This invention relates to a tuning fork resonator using an elastic coupling between the fundamental vibration of a flexural mode and the fundamental vibration of a torsional mode, and more particularly to the positions of masses for adjusting frequencies of the two modes.
Recently, a tuning fork quartz resonator with improved frequency-temperature characteristic (referred to as f-T characteristic hereafter) using an elastic coupling between the flexural mode and the torsional mode has been proposed. This tuning fork quartz resonator has become popular since it may serve as a quartz resonator for wristwatches with high accuracy capable of indicating yearly rate of a comparatively low frequency.
To improve the f-T characteristic of the flexural mode using the elastic coupling of the two modes, the frequency difference (referred to as .delta.f hereafter) of the two modes should be set at a suitable value. When the length and width of the tuning fork arms are respectively l, w, and thickness of the resonator is t, the frequency of the flexural mode (referred to as f.sub.F hereafter) and the frequency of the torsional mode (referred to as f.sub.T hereafter) are respectively proportional to w/l.sup.2 and t/(lw). Therefore, to set .delta.f at a suitable value, the thickness t of the resonator should be set at a suitable value. Since, however, the amount of change in f.sub.T by the thickness t is extremely large, it is nearly impossible to set .delta.f at a suitable value only by varying the thickness t.
For that, the adjustment of the frequency difference .delta.f (referred to as .delta.f adjustment hereafter) has been attempted by the addition or reduction of masses on a tuning fork resonator. Frequency adjustment by addition or reduction of masses has two purposes; namely, one is the frequency adjustment by setting a frequency f.sub.F of the flexural mode, which is the main mode, at a desired value, the other is the frequency adjustment by adjusting the frequency difference .delta.f between the flexural mode and the torsional mode. In the latter case, it is desirable that the frequency of one mode scarcely changes while the other mode largely changes by the addition or reduction of the masses.
FIG. 1 shows a conventional embodiment of the positions of masses added or reduced at a tuning fork quartz resonator using an elastic coupling between a secondary flexural mode and a fundamental torsional mode. Numeral 11 denotes a tuning fork quartz resonator, 12 and 13 are masses added or reduced at the tips of the tuning fork arms, 14 and 15 denote masses added or reduced at the position l' which is spaced from the resonator crotch by 0.77 l when the length of the arms is l. x, y' and z' respectively denote the width, length and thickness directions of the resonator and also denote the directions of the electrical axis x, the mechanical axis y rotated around the x axis, and the optical axis z rotated around the x axis.
FIG. 2 shows the displacement in the x direction of the secondary flexural mode on line AB on the tuning fork arms in FIG. 1. When the length of the tuning fork arms is l, the displacement of the position l' away from the point A by about 0.77 l is zero. Accordingly, f.sub.T can be largely changed with scarcely changing f.sub.F by addition or reduction of the masses 14 and 15 in FIG. 1.
The length of the arms of the tuning fork quartz resonator using the coupling between the secondary flexural mode and the fundamental torsional mode should be, however, longer than that of the tuning fork quartz resonator using the coupling between the fundamental flexural mode and the fundamental torsional mode when the frequencies of each of the flexural modes are the same. Moreover, the thickness of the resonator should be larger to enable the elastic coupling between the flexural mode and the torsional mode. Accordingly, a method of using the elastic coupling between the secondary flexural mode and the fundamental torsional mode is disadvantageous in that the dimension of the resonator becomes larger and because it takes a comparatively long time to make the resonator by etching using photolithography and thus is not suitable for mass production.